1) Should I connect Wireless access point to a trunk port on the
That depends. Are you using a single SSID and comfortable with the WAP management address on the same network as the wireless users? If so, an access interface should work. If you want to offer multiple SSIDs, or you want to manage the WAP at an address on a different network, then you need to connect the WAP to a trunk interface.
2) Is WAP technically a router or a switch.
A WAP is a bridge, like a switch. Unlike a switch, a WAP is a translating bridge; it must translate the layer-2 protocols between ethernet (IEEE 802.3) and Wi-Fi (IEEE 802.11). Those two protocols use different frames, and the WAP must convert them. In the old days, we had translating bridges for ethernet and token ring (IEEE 802.5). An ethernet switch is a transparent bridge.